Problem: Solve for $n$. $\left(8^n\right)^{3}=8^6$ $n=$
Answer: The general rule for powers of powers is $\left(x^m\right)^{n}=x^{m\cdot n}$. Let's expand the powers for $ \left({8^n}\right)^{{3}}=8^6}$. $\begin{aligned} \left({8^n}\right)^{3}&=\underbrace{{8^n\cdot 8^n \cdot 8^n}}_{\text{3 times}} \\\\\\ &=\underbrace{ \underbrace{{8 \cdot 8}}_{n\text{ times}} \cdot \underbrace{{8 \cdot 8}}_{n\text{ times}} \cdot \underbrace{{8\cdot 8}}_{n\text{ times}}} _{\text{3 times}} \\\\ &=\underbrace{8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8}_\text{6 times}} \\\\ \end{aligned}$ $n = 2$